MATH AGAIN?

One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days. How long will it take the two pumps, working together, to empty the pool?
The first pump's rate is
1/5
The second pump's rate is
1/8
The combined pumps rate is
13/40
It will take the two pumps
days to empty... show more One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days. How long will it take the two pumps, working together, to empty the pool?

One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days.
How long will it take the two pumps, working together, to empty the pool?
The first pump's rate is 1/5. The second pump's rate is 1/8.
The combined pumps rate is 13/40
It will take the two pumps 3.07..days to empty the pool together.

Pay attention to the units. What are the units in a rate of "1/5"? It's one pool per 5 days.

So when you add the rates (the proper thing to do), you get 13/40, meaning 13 pools in 40 days, or since 13/40 = 1/(40/13), it's one pool per 40/13 days = 3 1/13 days = 3.076923... days (last 6 digits repeat).

The first pump could empty the pool 8 times in 40 days, and the second pump could empty the pool 5 times in 40 days.
Together they could empty the pool 13 times in 40 days, so (dividing through by 13) it will take the two pumps 40/13
days to empty the pool together.

"One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days."
"How long will it take the two pumps, working together, to empty the pool?"
(5*8) / (5+8) = 40/13 days (about 3 and 1/13 day)